In a phone call with Egyptian vice president for foreign affairs, Mr Hague stressed the need for dialogue and reconciliation between all political parties including Mr Morsi's Muslim Brotherhood.
The Foreign Secretary also condemned the excessive use of force by security services as well as attacks against them.
Mr Hague said: "We want to see a peaceful resolution that will bring an urgent end to the current bloodshed. In my view, this should involve a process of dialogue and reconciliation between all political parties in Egypt, including the Muslim Brotherhood.
"I also called for the release of all political detainees, including President Morsi, unless there are criminal charges to be made against them, and emphasised that it is vital that any charges are not politically motivated."
The European Union's foreign policy chief Baroness Ashton has said deposed Egyptian President Mohamed Mursi was "well" and had access to television and newspapers when she visited him.
She spoke to journalists after meeting Mr Mursi at an undisclosed location last night.
European Union foreign policy chief Cathy Ashton has met ousted Egyptian president Mohamed Morsi and held two hours of "in depth" discussions with him, her spokeswoman, Maja Kocijancic, said.
Supporters of Egypt's ousted president Mohammed Morsi marched towards security headquarters in Cairo on Monday night, raising fears of new clashes as the EU's foreign policy chief met local officials, according to the Agence France Presse agency.
The marches came despite a warning from the National Defence Council late Sunday that it would take "decisive and firm action" against demonstrators if they went beyond their right to peaceful protest.
The Egyptian authorities have ordered that deposed president Mohamed Morsi be detained for 15 days over an accusation he conspired with Hamas in a series of prison breaks in Egypt in 2011, Reuters have reported.
Seven people were killed and 261 wounded in Cairo when supporters of Mohamed Morsi clashed with the deposed president's opponents and security forces overnight, the head of Egypt's emergency services said.
Mohamed Sultan told Reuters two people had been killed at a bridge in central Cairo and five more in the capital's Giza district.
Police fired tear gas in central Cairo last night when protesters calling for the reinstatement of the ousted Islamist president, Mohamed Morsi, scuffled with drivers and passers-by annoyed that they had blocked major roads.
Supporters of Morsi, Egypt's first freely elected president, threw rocks at police near Ramses Street, one of the capital's main thoroughfares, and on the Sixth of October Bridge over the Nile in the first outbreak of violence in Egypt in a week.
Egyptian security forces fired tear gas in central Cairo after scuffles broke out between supporters of ousted Islamist president Mohamed Morsi and locals in the area of Ramses Street, eye witnesses said.
It was the first violent confrontation involving pro-Morsi protesters for a week. Last Monday, 53 pro-Morsi demonstrators were killed outside the Republican Guard compound in Cairo. Four soldiers also died in the clash.
The United States has called for the release of ousted Egyptian president Mohamed Morsi, who has been held in custody by the army since last week.
Thousands of Muslim Brotherhood supporters today took to the streets of Cairo to demand Morsi's reinstatement.
ITV News Middle East Correspondent John Ray reports.